534 Proceedings of Philosophical Societies, [Maech^, 



The experiments contained in the first meiBoir of M. Biot 

 proved that the thicknesses of the plates which polarize such or 

 such a colour have a constant ratio with the thin plates which 

 reflect the same colours in the coloured rings. From the new 

 phenomena which we have stated it is evident that this property 

 is not confined to thin plates ; but that it extendis to every dis- 

 tance across the thickness of bodies. This is the second fact 

 which serves as a basis to the theory of M. Biot. 



He explained this theory in a fifth memoir read to the Class 

 on the 7th of December, 1812. " I do not propose/' says M. 

 Biot, to seek an hypothesis to explain the facts which I have 

 observed, I wish only to compare them together, and to reduce 

 them by mathematical consideration to a single fact, which will 

 be the abridged expression of them, and from which we may 

 afterwards draw by calculation, not only the phenomena w^iich I 

 have noticed, but all those which may result from their combi- 

 nation." 



This general property, which includes all the others, is the 

 following. Let us suppose that a plate of sulphate of lime, of 

 mica, or of rock crystal, cut parallel to the axis, is exposed 

 perpendicularly to a polarized ray, so that its axis of crystalliza- 

 tion makes an angle i with the plane of the polarization of the 

 ray; the molecules of light, in falling upon that plane, will 

 penetrate at first to a small depth without undergoing changes in 

 their polarization; but at a certain limit, different for the mole- 

 cules of different colours, they will begin to oscillate, like 

 magnetic needles, round their centre of gravity. The magnitude 

 of these oscillations, which will be o and 2 i, will bring by turns 

 their axes of polarization into the azimuths o and 2 i; but as the 

 celerity of the oscillations is not the same for molecules of 

 different colours, it follows that they do not all arrive at the same 

 time at these two limits, and this occasions the difference of 

 colour which w^e observe in them. Finally, the inequalities of 

 their celerity mixing more and more with each other, they will 

 at last form two white pencils, situated in the same straight line, 

 one of which will have its axis of polarization turned in the 

 azimuth 2 i, while the other will be in the azimuth o, so that 

 the last will appear to have preserved its primitive polarization. 

 M. Biot determines the rapidity of these oscillations for the 

 different molecules of light. He fixes the depth at which they 

 commence, and determines generally all their laws. He even 

 calculates that of the force which produces them, and shows 

 from the phenomena that it is proportional to the angle formed at 

 each instant by the axis of polarization of the luminous mole- 

 cules, and the axis of the crystalline plate : and as the time of 

 these oscillations may be calculated from the thickness which the 

 light traverses during them, there results a relation between the 



